<1. Spiral Wave>
Spiral waves which are the premise of the present application will be described, with light waves as an example. In a coherent optical system, the phase of propagating light waves is uniquely determined. A plane having an equal phase is called a wavefront, and waves are classified into plane waves (see FIG. 1a) or spherical waves depending on the shape of the wavefront.
On the other hand, there is a case of having a singularity in which the phase is not uniquely determined. The example thereof is a spiral wave in which an equiphase surface forms a spiral shape around a certain axis (generally, it is parallel to an optical axis). The spiral wave is a wave having a phase state in which the phase is changed by an integral multiple of 2π when the azimuth is rotated one round, with the singularity as a center (the axis of the spiral), when viewed respectively from a plane perpendicular to the propagation direction of the wave. The change amount of the phase of an integral multiple of 2π corresponds to an integral multiple of change in wavelength in the propagating light waves.
A spiral wave 21 of which a phase changes by 2π when the azimuth is rotated one round is illustrated in FIG. 1b. In the present application, the wave in a state of changing by 2π is referred to as a spiral wave of “helicity 1”. As is apparent from FIG. 1b, the on-axis of the helical axis 22 becomes a singularity of a phase and it is not possible to determine the phase in the on-axis.
A spiral wave 24 of “helicity 2” of which phase changes by 4π when the azimuth is rotated one round is illustrated in FIG. 1c. The wavefront changes by two wavelengths when the azimuth is rotated one round considering propagating light waves. Since there is no possibility that the wavelength is extended, considering a wavefront which is shifted by exactly a half-period as illustrated in FIG. 1d, the phase distribution illustrated in FIG. 1e obtained by combining both wavefronts is considered as a model of a spiral wave of helicity 2. Similar to the case of helicity 1, the spiral wave has a singularity (helical axis 22) at which the phase is not uniquely determined. In other helicities, a combination of plural wavefronts is considered by matching the helicities, similar to FIG. 1e. 
FIG. 2A is a diagram of a particle model depicting converging spiral waves as flow lines 27. Briefly, considering the flow lines as a particle track, it may be considered that the track (flow lines) is drawn in the direction perpendicular to the wavefront. As the helicity increases, the degree of twisting increases.
In FIG. 2B, an intensity distribution of the wave in a convergence surface (diffractive surface 94) is depicted, and the spiral wave becomes a ring-shaped spot 97 at the convergence point. This ring shape is expressed in a Bessel function (cylinder function). As illustrated in FIG. 2A, the converging spiral waves (particles) propagate while twisted, thereby transmitting momentum in a direction perpendicular to the propagation direction.
For example, in the case of placing a sample on the convergence surface 94 (the plane illustrated in FIG. 2B), it is possible to transmit the momentum in the direction of the plane to the sample. Thus, the feature of the spiral wave is capable of transmitting the momentum. In the example illustrated in FIG. 2B, the momentum of rotation is transmitted in a counterclockwise direction. In addition, the combined sum of the momentum in all directions becomes zero.
The spiral wave, which is referred to as Laguerre-Gaussian beam or optical vortex in optics, is a light wave propagating while maintaining the orbital angular momentum, and can exert force on an equiphase surface (wavefront). Therefore, it is possible to provide momentum to an irradiation target, and this is practically used as, for example, manipulation techniques such as optical tweezers which manipulate particles of a size of about a cell, laser processing, or super-resolution microspectroscopy. In addition, since multiple orbital angular momentums can be inherent in a portion of the spiral axis which is a phase singularity, this attracts attention in the field of quantum information communication. In addition, new technological evolution is expected in physical property analysis and structural analysis, such as analysis of a stereoscopic image of a magnetization state or an atomic arrangement in X-rays.
In addition, a topological charge (being inherent of orbital angular momentum) referred to herein has an advantage in selecting the strength of spiral winding. Hereinafter, for the sake of simplicity, the topological charge is also referred to as “helicity”.
As described above, in the case of the spiral wave in electron beams (electron spiral wave), the electron beams propagate while maintaining the orbital angular momentum, such that it is expected to produce applications as an electron beam probe (incident beam) which is not present as of now. The examples of the application are of a highly sensitive or three-dimensional state measurement in magnetization measurements, and observation of high-contrast and high-resolution protein molecules or sugar chains. Especially, in the magnetization observation, the electron beam has a fundamental disadvantage with no sensitivity for parallel magnetization to the direction of propagation, but there is a possibility of observing the magnetization of the electron beam in a propagation direction in the electron spiral wave.
Moreover, there is a possibility of application not only to the observation, but also to processing and magnetization control using the orbital angular momentum. Therefore, it has started to receive attention as a probe of an electron beam apparatus of the next generation, along with the spin-polarized electron beam. In other words, regardless of a wave field and particles, there is a possibility as a new probe, and application and development are also contemplated with respect to X-rays, neutron beams, and ion beams, in addition to light waves and electron beams which are described herein.
<2. Generation of Spiral Wave>
Two types of methods are implemented to generate a spiral wave. One of them is a method of using that a thin film having a spiral shape (thickness distribution) is irradiated with a plane wave, and the phase distribution of the transmitted wave becomes a spiral shape due to the thickness of the film. The other thereof is a method of using a diffraction wave by the diffraction grating including edge dislocation called a fork-type grating (edge dislocation diffraction grating) (FIG. 3, and Non-Patent Document 1). In the first method of irradiating the thin film with a plane wave, in a case where the wavelength is extremely short such as electron waves, it is difficult to produce a thin film with a spiral shape, such that a second method of using an edge dislocation diffraction grating becomes popular at present.
Next, a description will be given on the second method of using a diffraction grating including the edge dislocation (edge dislocation diffraction grating) with reference to FIG. 3. The spiral wave 21 (a wave of which the equiphase surface forms a spiral shape) which is generated as a diffraction wave from an edge dislocation diffraction grating 91 forms ring-shaped diffraction spots 97, instead of a common point-shaped diffraction spot 99, in the diffraction image 9. If it is possible to spatially separate one of the ring-shaped diffraction spots in the diffractive surface 94, it is possible to retrieve a desired spiral wave 21. The generation of the spiral wave can control the degree of the helicity depending on the number of orders of the edge dislocations. In addition, it is possible to control the positive and negative (the right-handedness or left-handedness of the spiral) of the helicity by the positive and negative of the Burgers vector of the edge dislocations.
FIG. 4A is an electron microscope image of a third-order edge dislocation grating 91 which is actually produced. The edge dislocation grating 91 is produced by performing processing on a silicon nitride membrane (thickness 200 nm) by a focusing ion beam apparatus. Three gratings are inserted from the upper side of FIG. 4A, and are concentrated in the central portion. In other words, the concentrated portion is located in a position of the core of the edge dislocations, and the order of FIG. 4A is a third order. The order of the edge dislocation and the degree of the generated spiral wave basically match. However, in a case where the contrast of the diffraction grating is high and high-order diffraction waves are obtained, spiral waves are also generated which has the helicity of a product value which is obtained by multiplying the order of the edge dislocation and the order of the diffraction wave.
FIG. 4B is a small angle electron diffraction image 9 (recorded in a camera length of 150 m) which is obtained when a diffraction grating of FIG. 4A is irradiated with an electron beam of an acceleration voltage 300 kV. The ring-shaped diffraction spots 97 of ±1 orders, ±2 orders, and ±3 orders are observed on the left and right of the zero-order spot 99 of the central portion, and the ring diameter increases as the diffraction order increases. Thus, it can be seen that spiral waves having the helicities of ±3 orders, ±6 orders, and ±9 orders are generated. In other words, the ring diameter of the diffraction spot represents the helicity of the spiral wave directly. Thus, it is possible to generate plural types of spiral waves 21 from the diffraction grating 91, which includes one edge dislocation.